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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
M. Mitjana
Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya
Electrical & Electronics Engineering

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On middle cube graphs C. Dalfo; M. A. Fiol; M. Mitjana
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (2015): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2015.3.2.3

Abstract

We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors).
Co-Authors C. Dalfo M. A. Fiol